Research Papers

Modeling of 2D and 3D Assemblies Taking Into Account Form Errors of Plane Surfaces

[+] Author and Article Information
Serge Samper

SYMME, Polytech’ Savoie, Université de Savoie, B.P. 80439-74944, Annecy le Vieux Cedex, Franceserge.samper@univ-savoie.fr

Pierre-Antoine Adragna

SYMME, Polytech’ Savoie, Université de Savoie, B.P. 80439-74944, Annecy le Vieux Cedex, Francepierre-antoine.adragna@univ-savoie.fr

Hugues Favreliere

SYMME, Polytech’ Savoie, Université de Savoie, B.P. 80439-74944, Annecy le Vieux Cedex, Francehugues.favreliere@univ-savoie.fr

Maurice Pillet

SYMME, Polytech’ Savoie, Université de Savoie, B.P. 80439-74944, Annecy le Vieux Cedex, Francemaurice.pillet@univ-savoie.fr

J. Comput. Inf. Sci. Eng 9(4), 041005 (Nov 02, 2009) (12 pages) doi:10.1115/1.3249575 History: Received July 09, 2008; Revised February 18, 2009; Published November 02, 2009; Online November 02, 2009

The tolerancing process links the virtual and the real worlds. From the former, tolerances define a variational geometrical language (geometric parameters). From the latter, there are values limiting those parameters. The beginning of a tolerancing process is in this duality. As high precision assemblies cannot be analyzed with the assumption that form errors are negligible, we propose to apply this process to assemblies with form errors through a new way of allowing to parameterize forms and solve their assemblies. The assembly process is calculated through a method of allowing to solve the 3D assemblies of pairs of surfaces having form errors using a static equilibrium. We have built a geometrical model based on the modal shapes of the ideal surface. We compute for the completely deterministic contact points between this pair of shapes according to a given assembly process. The solution gives an accurate evaluation of the assembly performance. Then we compare the results with or without taking into account the form errors. When we analyze a batch of assemblies, the problem is to compute for the nonconformity rate of a pilot production according to the functional requirements. We input probable errors of surfaces (position, orientation, and form) in our calculus and we evaluate the quality of the results compared with the functional requirements. The pilot production then can or cannot be validated.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 4

Functional requirement of the assembly

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Figure 1

Mode shapes of a free BC square

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Figure 2

Generation of the modal statistical characteristics of a virtual batch

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Figure 3

Generation of a virtual batch based on statistical characteristics

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Figure 6

Mode shapes of a free-free beam

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Figure 7

Modal parameters

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Modal coefficients of the difference surface

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Contact facet determination

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Figure 10

Comparison between the assembly methods

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Figure 11

Deviation SDTs of associated surfaces

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Figure 12

Resulting SDT and functional requirements of one assembly

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Figure 13

Conformity of a set of 100 assemblies

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Figure 14

Surfaces A1 and A2 and assembly of associated surfaces

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Figure 15

Contact facet on the assembly

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Figure 16

3D view of the contact

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Figure 17

Assembled surfaces and contact points: a 2D view

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Figure 18

FRB domain and assembly verifications

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Figure 19

Functional requirement (FRB) 3D Domain and SDT of assemblies



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